CE 170: Environmental Engineering

Notes on Coagulation/Flocculation (Johnston)

As you recall from the classroom discussion, the settling velocity of a particle depends n its size (Stokes’ Law). Very small particles (colloids) don’t settle fast enough to make removal by sedimentation practical. We don’t have the space to build settling tanks with detention times of days or weeks. Yet we need to remove these particles from drinking water because they cause turbidity. (Remember the filtrate in the TSS lab?) The turbidity standard for drinking water is 0.5 NTU, so we must be efficient about removing these particles.

One strategy to increase settling rates is to cause the small particles to clump together in larger structures, called “flocs”. Normally, colloidal particles don’t want to clump together because their respective surface charges cause them to repel each other. In coagulation, we use chemical means to either: (1) reduce the surface charge, (2) bind the particles to each other using polymers, or (3) intentionally form large precipitates which sweep the smaller particles out of the water. Mixing is an important aspect of this process. A rapid mix is needed initially to bring the chemical into contact with the particles. Afterwards, a slow mix is needed to cause the particles to contact each other and form flocs. The slow mixing process is usually called flocculation.

Design and operation of coagulation/flocculation processes (the words are joined this way because almost never is one used without the other), depend on jar testing. The success of chemical processes depends on many factors such as the nature of the particles (e.g., organic or mineral), the number and size distribution of particles, temperature, pH, and the presence of dissolved substances that interfere with precipitation. Rather than try to measure these parameters, some of which can change relatively quickly with time, it is more practical to perform a miniature process in a jar and “scale-up” the results. Similarly, providing the proper amount of mixing is not easy to predict. If too little mixing is provided, there will be insufficient contact between particles for build large flocs. If too much mixing is provided, the hydrodynamic forces in the water will break the flocs up. How much is “too much” depends on the strength of the flocs, which in turn depends on the chemistry and interactions between the the particles and the coagulants (i.e., the chemicals). Again, actually doing the mixing in a jar test is the most practical approach in most cases.

In this lab, we will perform a typical jar test for choosing a coagulant dose and a mixing intensity, measured by a parameter called “velocity gradient”.

Velocity Gradient and Power Equations

Velocity gradient is a measure of the degree of mixing of a system. The name derives from the idea that a well-mixed system (one with a lot of turbulence) has a large change of velocity with respect to distance (the derivative of the velocity with respect to distance or “gradient”). Practically, it is measured by the power input per unit volume (P/V) divided by the viscosity, raised to the 0.5 power.

where:

G = velocity gradient (s-1)

P = power dissipated in the water (W or ft-lb/s)

 = viscosity (N-s/m2 or lb-s/ft2)

V = volume (m3 or ft3)

For the paddle-type mixers being used in lab, the power input to the water can be estimated by the drag force times the angular velocity. Assuming turbulent conditions and doing a bunch of algebra, you can derive:

where:

P = power (ft-lb/s)

n = rotational speed (rev/s)

D = diameter of paddle (ft)

 = specific weight of water (lb/ft3)

g = acceleration due to gravity (32.17 ft/s2)

KT = empirical constant = 2.4 for Phipps and Bird jar test mixer used in this lab

(KT was calculated from data provided by Phipps and Bird.)

These are the equations to use in determining G for your mixers. Because of the empirical constant KT, the power calculations must be done in U.S. units and then converted for the G calculation (useful conversions: 1.3558 W per ft-lb/s, Pa = N/m2).

References for G calculations:

McCabe, W. L., J. C. Smith, and P. Harriott, Unit Operations of Chemical Engineering, 5th ed., McGraw-Hill, 1993.
Rushton, J. H., "Mixing of Liquids in Chemical Processing", Industrial and Engineering Chemistry, American Chemical Society, v 44, n 2, p 2931, Dec 1952.
Rushton, J. H. and J.Y. Oldshue, "Mixing -- Present Theory and Practice", Chemical Engineering Progress, v 46, n 4, p 161, April 1953.
Reynolds, T. D. and P.A. Richards, Unit Operations and Processes in Environmental Engineering, PWS Publishing Company, 1996.
Wagner, E.G., "Jar Test Instructions, Conduct of Jar Tests and the Important Information Obtained", booklet from Phipps and Bird, 8741 Landmark Rd., Richmond, VA23228, July 1993.